An Evening Spent with Bill van Zwet

Willem Rutger van Zwet was born in Leiden, the Netherlands, on March 31, 1934. He received his high school education at the Gymnasium Haganum in The Hague and obtained his Masters degree in Mathematics at the University of Leiden in 1959. After serving in the army for almost two years, he obtained his Ph.D. at the University of Amsterdam in 1964, with Jan Hemelrijk as advisor. In 1965, he was appointed Associate Professor of Statistics at the University of Leiden and promoted to Full Professor in 1968. He remained in Leiden until his retirement in 1999, while also serving as Associate Professor at the University of Oregon (1965), William Newman Professor at the University of North Carolina at Chapel Hill (1990--1996), frequent visitor and Miller Professor (1997) at the University of California at Berkeley, director of the Thomas Stieltjes Institute of Mathematics in the Netherlands (1992--1999), and founding director of the European research institute EURANDOM (1997--2000). At Leiden, he was Dean of the School of Mathematics and Natural Sciences (1982--1984). He served as chair of the scientific council and member of the board of the Mathematics Centre at Amsterdam (1983--1996) and the Leiden University Fund (1993--2005).Comment: Published in at http://dx.doi.org/10.1214/08-STS261 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

STM Studies of TbTe3: Evidence for a fully Incommensurate Charge Density Wave

We observe unidirectional charge density wave ordering on the cleaved surface of TbTe3 with a Scanning Tunneling Microscope at ~6 K. The modulation wave-vector q_{CDW} as determined by Fourier analysis is 0.71 +/- 0.02 * 2 pi/c. (Where c is one edge of the in-plane 3D unit cell.) Images at different tip-sample voltages show the unit cell doubling effects of dimerization and the layer below. Our results agree with bulk X-ray measurements, with the addition of ~(1/3) * 2 pi/a ordering perpendicular to the CDW. Our analysis indicates that the CDW is incommensurate.Comment: 4 pages, 4 figure

QCD traveling waves beyond leading logarithms

We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the Balitsky-Kovchegov-Kuraev-Lipatov kernel at next-to-leading logarithmic accuracy, conveniently regularized by different resummation schemes. Traveling waves allow to define "universality classes" of asymptotic solutions, i.e. independent of initial conditions and of the nonlinear damping. A dependence on the resummation scheme remains, which is analyzed in terms of geometric scaling properties.Comment: 10 pages, 5 figures; typos corrected, references updated, final Phys.Rev. D versio

Gas-liquid critical point in ionic fluids

Based on the method of collective variables we develop the statistical field theory for the study of a simple charge-asymmetric $1:z$ primitive model (SPM). It is shown that the well-known approximations for the free energy, in particular DHLL and ORPA, can be obtained within the framework of this theory. In order to study the gas-liquid critical point of SPM we propose the method for the calculation of chemical potential conjugate to the total number density which allows us to take into account the higher order fluctuation effects. As a result, the gas-liquid phase diagrams are calculated for $z=2-4$. The results demonstrate the qualitative agreement with MC simulation data: critical temperature decreases when $z$ increases and critical density increases rapidly with $z$.Comment: 18 pages, 1 figur

Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J1 and J2, which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z2 spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J2, we find a Neel phase, a plaquette valence-bond (PVB) phase with a finite spin gap, and a possible spin liquid in a small region of J2 between these two phases. From the finite-size scaling of the magnetic order parameter, we estimate that the Neel order vanishes at J2/J1~0.44. For 0.5<J2/J1<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J2/J1<0.5, spin order, dimer order, and spin gap are small on finite-size systems and appear to scale to zero with increasing system width, which is consistent with a possible gapless SL or a near-critical behavior. We compare and contrast our results with earlier numerical studies.Comment: 11 pages, 17 figures, and 1 tabl

Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found evidence for a 2D spin liquid in proximity to the metal-insulator transition. A Gutzwiller wavefunction study of the triangular lattice Heisenberg model with appropriate four-spin ring exchanges has found that the projected spinon Fermi sea state has a low variational energy. This wavefunction, together with a slave particle gauge theory, suggests that such spin liquid possesses spin correlations that are singular along surfaces in momentum space ("Bose surfaces"). Signatures of this state, which we refer to as a "Spin Bose-Metal" (SBM), are expected to be manifest in quasi-1D ladder systems: The discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg strip (zigzag chain). Using DMRG, variational wavefunctions, and a Bosonization analysis, we map out the full phase diagram. Without ring exchange the model is equivalent to the J_1 - J_2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess particular singular wavevectors and allow us to identify this phase as the hoped for quasi-1D descendant SBM state. We derive a low energy theory and find three gapless modes and one Luttinger parameter controlling all power laws. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 VBS or a period-4 Chirality order, which we discover in the DMRG; we also find an interesting SBM state with partial ferromagnetism.Comment: 30 pages, 23 figure

Geometric scaling as traveling waves

We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky- Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.Comment: 4 pages, 1 figure. v2: references adde

Universality and tree structure of high energy QCD

Using non-trivial mathematical properties of a class of nonlinear evolution equations, we obtain the universal terms in the asymptotic expansion in rapidity of the saturation scale and of the unintegrated gluon density from the Balitsky-Kovchegov equation. These terms are independent of the initial conditions and of the details of the equation. The last subasymptotic terms are new results and complete the list of all possible universal contributions. Universality is interpreted in a general qualitative picture of high energy scattering, in which a scattering process corresponds to a tree structure probed by a given source.Comment: 4 pages, 3 figure